Question

Найдите основания трапеции, если средняя линия равна 16см иделится диагональю на части, разность которых равна 6см.

Answer 1

(а+в)/2=16⇒а+в=32
(а-в)/2=6⇒а-в=12⇒а=12+в
12+в+в=32⇒2в=20⇒в=10
а=12+10=22
ответ:22,10

Answer 2

Finding the Bases of a Trapezoid

To find the bases of a trapezoid when the median is 16 cm and divides the diagonal into two parts, the difference of which is 6 cm, we can use the following approach:

1. Identify the Given Information: - Median length: 16 cm - Difference of the parts of the diagonal: 6 cm

2. Use the Median Property: - The median of a trapezoid is equal to the average of the bases. Therefore, the sum of the bases is twice the length of the median.

3. Calculate the Bases: - Let's denote the lengths of the bases as \( b_1 \) and \( b_2 \). - According to the given information, the sum of the bases is \( 2 \times 16 = 32 \) cm. - Additionally, the difference of the parts of the diagonal is 6 cm.

4. Solve for the Bases: - We can set up a system of equations to solve for the bases using the sum and difference of the bases. - Let's denote the lengths of the parts of the diagonal as \( d_1 \) and \( d_2 \). - We have the equations: - \( b_1 + b_2 = 32 \) (from the median property) - \( |d_1 - d_2| = 6 \) (from the given difference of the parts of the diagonal)

5. Solving the System of Equations: - By solving the system of equations, we can find the lengths of the bases \( b_1 \) and \( b_2 \).

6. Conclusion: - Once the system of equations is solved, we will have the lengths of the bases of the trapezoid.

Let's proceed with solving the system of equations to find the lengths of the bases.